Definitions
How can we define tangent using sine and cosine?
The tangent of an angle is defined as the quotient between its sine and its cosine.
tan(x)=sin(x)/cos(x)
How can we represent the angle of 90° in radians?
pi/2 or approximately 1.57 radians.
What is the value of sin(30°)?
1/2
In the equation of the function f(x)=a sin[b(x-c)]+d, how does the constant c affect the graph of the function?
It represents a horizontal translation, also known as phase shift.
How do we define the sine of an angle in a right-angled triangle?
Sine is given by the length of the opposite side divided by the length of the hypothenuse.
Which trigonometric function is positive in the first and fourth quadrants?
Cosine
What is the value of cos(90°)?
Zero
How can we change the equation to make the amplitude of the function f(x)=sin(x) be 2?
Multiplying the right-hand side by 2, that is, f(x)=2sin(x).
What is the Unit Circle?
The circle we use to represent angles. Its center is the origin of the coordinate plane and its radius is 1.
How can we represent the angle of 135° in radians?
3pi/4 or approximately 2.356 radians.
What is the exact value of sin(300°)?
-(√3)/2
What is the equation of the center line of the function f(x)=3sin(x+1)-2? (Equation, not value!)
y=-2
How did we define sine and cosine in the Unit Circle?
Sine is the y-coordinate of the point in the circle that is the terminal point of the angle.
Cosine is the x-coordinate of the point in the circle that is the terminal point of the angle.
What's the acute angle that is co-terminal to 732°?
12°
Given that 0<x<360°, what are all values of x such that sin(x)=-1/2?
210° and 330°
Write the equation of a sine wave function that has a maximum point at (0, 3).
Sample answer: f(x)=3sin(x+pi/2)
Explain the definition of radians and why 2pi radians corresponds to 360°.
One radian is the angle that covers the distance of the radius of the circle in the circumference. Since the circumference measures 2pi times the radius, there are 2pi radians in a full turn (360°).
What is, in radians, the reference angle for the angle 260°?
4pi/9 or approximately 1.396 radians.
Given that 0<x<360°, what are all values of x such that sin(x)=-√5? Explain.
There are no values of x such that sin(x)=-√5, because -√5<-1.
Draw the graph of the function y=3sin[2(x+pi/4)]-1. Show the coordinates of at least three points.
(You have 1 minute and 30 seconds to solve this one)